Question

Gaseous cyclobutene isomerizes to butadiene in a first order process which has a ${}^{'}k_{}^{'}$ value of $3.3\times 10^{- 4}s^{- 1}$ at $153^\circ C$ . The time in minutes it takes for the isomerization to proceed $40\%$ to completion at this temperature is ______. (Rounded off to the nearest integer)

Answer 1

For first order Reaction :-
$t=\frac{2 . 303}{k}log\left[\frac{100}{100 - x}\right]$
$x=40,k=3.3\times 10^{- 4}$
$t=\frac{2 . 303}{3 . 3 \times 10^{- 4}}log\left[\frac{100}{60}\right]$
$t=\frac{2 . 303}{3 . 3 \times 10^{- 4}}\times 0.22$
$t=0.15353\times 10^{4}$
$t=1535\sec=25.6 \, Min \simeq 26\,\min$ .